### Vector Addition: Assessment Question #### Which of the following statements are correct? - [ ] Adding two vectors creates a new "resultant" vector. - [ ] When adding parallel vectors, the resultant vector is the sum of the magnitudes of the original vectors. - [ ] When adding perpendicular vectors, the resultant vector is the sum of the magnitudes of the original vectors. - [ ] Graphing calculators always report angles in degrees. - [ ] Vectors pointing in different directions cannot be subtracted. - [ ] A vector can be broken into x and y component vectors that sum to equal the original vector. - [ ] Multiplying a vector by a scalar changes the vector's magnitude and direction. **Explanation of Terms and Concepts:** 1. **Resultant Vector:** - The vector obtained from adding two or more vectors. The resultant vector gives the combined effect of the original vectors. 2. **Parallel Vectors:** - Vectors that have the same or exactly opposite direction. When parallel vectors are added, the magnitudes (lengths) sum algebraically, taking direction into account. 3. **Perpendicular Vectors:** - Vectors that are at right angles (90 degrees) to each other. The resultant magnitude is found using the Pythagorean theorem, not by simply adding magnitudes. 4. **Graphing Calculators:** - Tools used for plotting and analyzing data. They may report angles in degrees or radians, depending on the settings and type of calculator. 5. **Vector Subtraction:** - The process of finding a vector which, when added to a second vector, will result in a zero vector. Directions do not preclude subtraction. 6. **Component Vectors:** - A vector can be decomposed into two or more vectors (components) that add up to the original vector. The most common components are along the x-axis and y-axis. 7. **Scalar Multiplication:** - Multiplying a vector by a scalar (a real number) alters the vector's magnitude and can change its direction if the scalar is negative. **Graphical/Diagram Interpretation:** - This question set does not contain any graphs or diagrams. However, understanding geometric representations of vector addition, such as the tail-to-tip method, and calculations for vector components and magnitudes are crucial concepts. **Instructions:** For the following statements, select only those that are true. **Statements:** 1. [ ] The Cartesian coordinate (0, 1) would have a polar coordinate of r = 1, theta = 90 degrees. 2. [ ] When you know the x and y components (or sides) of a right triangle, you can obtain the hypotenuse using the Pythagorean theorem. 3. [ ] Converting polar coordinates of r = 5 and theta = 53 degrees to Cartesian coordinates gives x = 4, y = 3. (Be sure your calculator is in degree and not radian mode) 4. [ ] Converting polar coordinates of r = 5 and theta = 53 degrees to Cartesian coordinates gives x = 3, y = 4. (Be sure your calculator is in degree and not radian mode) 5. [ ] The unit circle diagram shows the angle pi radians, which corresponds to half a rotation around the circle, corresponds to and angle of 90 degrees. 6. [ ] A positive angle is measured from the positive x-axis in the CLOCKWISE direction, while a negative angle is measured from the positive x-axis in the COUNTER-CLOCKWISE direction.